Abstract
We investigate the field dependence of the gauge coupling functions of four-dimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes. In particular, we analyze the constraints imposed by holomorphicity and covariance under shift-symmetries of the bulk and brane axions. This requires introducing quantum corrections that necessarily contain Riemann theta functions on the complex torus spanned by the D7-brane Wilson line moduli. Our findings hint towards a new underlying geometric structure for gauge coupling functions in string compactifications. We generalize this discussion to a genuine F-theory compactification on an elliptically fibered Calabi-Yau fourfold. We perform the first general dimensional reduction of eleven-dimensional super-gravity and dualization to the F-theory frame. The resulting effective action is compared with the circle reduction of a four-dimensional \( \mathcal{N} \) = 1 supergravity theory. The F-theory geometry elegantly unifies bulk and brane degrees of freedom and allows us to infer non-trivial results about holomorphicity and shift-symmetries. For instance, we gain new insight into kinetic mixing of bulk and brane gauge fields.
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Corvilain, P., Grimm, T.W. & Regalado, D. Shift-symmetries and gauge coupling functions in orientifolds and F-theory. J. High Energ. Phys. 2017, 59 (2017). https://doi.org/10.1007/JHEP05(2017)059
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DOI: https://doi.org/10.1007/JHEP05(2017)059